Question 49
A polynomial $S(x) \in \mathbb{R}[x]$ is "simple" if it is divisible by $x$ but not by $x^2$. For the polynomial $P(x) \in \mathbb{R}[x]$, we know that there exists a simple polynomial $Q(x)$ such that $P(Q(x)) - Q(2x)$ is divisible by $x^2$. Prove that there exists a simple polynomial $R(x)$ such that $P(R(x)) - R(2x)$ is divisible by $x^{1401}$.